Welcome to the forums, SouthernMom! BigMark and HK47 had some good advice for you so I thought I'd throw in my two cents worth, too.
First, let me go over your four choices and then I'll dive into some of the survival-food specifics.
CHOICE 1 - EverSafe Complete Meal Kits
I'm not a big fan of the EverSafes. Wornick was one of the original companies to come out with civilian MREs (the Mil-Spec brand) but then they stopped making them. Then Katrina happened and they apparently (re)saw the value of emergency food for civilians and they started developing the EverSafes. At first, the EverSafes looked like they were going to be MRE-like. But then they started talking about a bowl-like meal. Then they introduced both the MRE-like meals and the bowl-like meals. And then they dropped the MRE-like meals. Personally, I don't think Wornick is committed to the civilian MRE market and I wouldn't spend my money with them. Wornick seems more interested in selling pallet-loads of expensive EverSafes to corporations and not very interested in selling a good emergency meal to civilians. We've had a couple of threads on the forums about EverSafes and if you haven't read through them yet, I'd encourage you to take a look. Just be warned - the product that CaptBob reviewed in one thread is no longer the one being sold by Wornick. That's too bad because I liked that one best.
CaptBob's EverSafe thread:
viewtopic.php?t=301
CHOICE 2 - MRE's - the ones on epicenter.
Are you talking about the individual MRE entrees on the Epicenter? I ask that because they also sell the Sopakco Sure-Paks that you have down as Choice #4. If you do mean the entrees, then it's really a toss-up between purchasing them from theepicenter.com, mrefoods.com, longlifefoods.com, or beprepared.com. Check out this thread for recent entree pricing from these guys:
viewtopic.php?t=560
Personally, I love stocking up on entrees when I can find them for a good price. Lots of entrees would make a good, portable emergency food supply but I would think you'd have to supplement it with some other things like crackers, spreads, etc. Sure, you could survive on entrees-only, but you'll probably start wishing for other things to add to meal.
CHOICE 3 - aPack MREs
I haven't tried the aPacks yet but from what I've seen and read, they look very promising. These are Ameriqual's entry into the civilian MRE market (finally!) and they look on par with Sopakco's Sure-Paks. Depending on pricing, if you're looking for the "reliability" of a civilian MRE (backed by someone you can sue if you get a bad one), then either the aPacks or Sure-Paks would be the way to go.
CHOICE 4 - Sure-Pak 12 MRE case with heaters
See my comments on Choice #3 above.
With all that said, I would add a 5th choice and this would be my number one choice:
CHOICE 5 - real MREs from eBay
I realize you said you want to be careful and that's why you ruled out MREs from eBay but I don't think it's that's risky. Here's why:
Price: there have been some deals on eBay lately - forget those $60 cases, I've seen some $30 cases with reasonable shipping. Lets say you could get a case for $45 total. A case of Sure-Paks is going to cost you around $65 plus shipping and a case of aPacks will be around $75 (shipping included) from mrefoods.com. That's a pretty big price savings by going with eBay.
Quality: as long as you're careful, you shouldn't have to worry about getting "old" MREs from eBay. Just pay attention to the menus and to the packed/inspection dates and you can be sure to score a case of MREs from 2005 or 2006. As for worrying about the storage conditions, yes, that's something you can't really tell but my experience has been that MREs hold up well despite varied storage conditions. I still have MREs from 1992 that I have no idea where or how they've been stored for the past 14 years and yet they're still good. I also have some MREs "fresh" from the Iraqi desert where I *know* they've been heat-stressed and yet they're still good (ok...for those, I won't keep them for years on end...maybe just a few years). But my point is that whatever you get from eBay is probably going to be just fine.
Variety: You're definitely going to get more food and more variety with a case of real MREs than you will with any civilian MRE. Even better, take a look at the how the pricing breaks down for this variety. If you go with longlifefood.com, 12 entrees will cost you $36 ($3 each). If you can get a case of MREs for $45 (only $9 more), not only do you get your 12 entrees, but you also get all the crackers, bread, sides, desserts, spoons, heaters, etc. I once priced out what it would cost to buy all the individual parts of a case of MREs from longlifefoods and it came up to about $120. So for $45, you're getting a lot of stuff that you just can't affordably buy any other way.
So that's my pitch. Military MREs are the cheapest option - canned food and stuff like that could be had cheaper. But for portable, ready-to-eat food, I don't think you can do any better. I've tried the heater meals and just wasn't impressed - especially for the cost.
One of your other concerns about your choices was breakfast. While there is an omelet MRE, I wouldn't count on it breakfast day after day. If it were me, I would try to get by on two MREs a day. I crack open an MRE for breakfast and eat the crackers, cheese or peanut butter (or even the pop tart if I got the right MRE) for breakfast and then finish off the entree and dessert for lunch. Then I'd have a whole MRE for dinner. This would cut down on the number of MREs you'd need.
Another option if you're concerned about breakfast is to stock up on some boxes of instant oatmeal and or breakfast bars/squares. If you can find a way to heat up water, you can have a hot instant breakfast of real breakfast food - and that stuff certainly won't cost as much as MREs.
As for kids and MREs, depending on how old your kids are and how much they eat, you might be able to get by with sharing one MRE between them. All the crackers, for instance, come as two 4"x4" crackers - the equivalent of 8 saltine crackers. While the Sqwincher drink mix you mentioned from the aPacks might be good for kids, I think the beverage base stuff from the MREs would work just the same - it's basically kool-aid.
In the end, depending on what you can afford to do financially, I would recommend trying all of your choices - buy a case of Eversafes, aPacks, Sure-Paks, and real MREs. This way, you'll definitely have a good supply of food and little experimenting with the family will show you what they like best. Maybe have an "MRE evening" every week where you sample the above cases to see what everyone likes. Personally, I think your kids will probably like the MREs. After all, the menus were designed to be appealing to 18 year old soldiers fresh away from home.
Something else to consider - a case of MREs weighs about 23 pounds - the MREs by themselves are about 21 pounds. If you're going to be eating two MREs per adult per day and two MREs for two kids per day, you'll get two days worth of food out of a case of MREs. That starts to be a lot of food to carry around. You might consider "field stripping" your MREs and just bringing along the components you need. For example, you might not need all the accessory pack and all the spoons and who knows what else. This might make it easier to pack and store for a trip.
), I could build my own. 
)
. They are at the right age to think its cool to have them for lunches and the gaggle of neighborhood boys are always needing to be fed. Heck, its cheaper than feeding them pizza when they descend like a pack of locusts and I'll just bogart a taste for myself. I will definitely field strip the pack and repackage as neccesary with the ole foodsaver to get these just right for lunches and dinners.
)